Teaching Macbeth this last semester, I saw a couple of things that I had never read being reference to Tolkien before. That doesn't mean that they haven't been, I am just unaware of anyone who has so made the connection.
It is well known, however, that the scene of Elsinore Wood coming to Macbeth was a scene that Tolkien didn't like, and so rewrote into his Ents' attacking Isengard. He speaks about this in the Letters and many others have repeated and mentioned it.
But there are two other places where I see at least a Tolkienian analogue. In Act 4.1 MacBeth has gone to the Weird sisters and asked them to tell him the future. Among the prophecies he receives is that "none of woman born Shall harm MacBeth." Macbeth then says, "Be bloody, bold, and resolute; laugh to scorn the power of man for none of woman shall harm Macbeth."
One can easily see the analogue. The Witch-King in Book V of Lord of the Rings is bloody, bold, and resolute placing faith in the prophecy "no living man may hinder me" (given in another form elsewhere as "not by the hand of man shall he fall."). The Witch King, hereafter Alf, is very confident because of this prophecy as MacBeth is. And as with most prophecies of this sort (like the Delphi Oracle) both Tolkien's and Shakespeare's prophecies turn on the interpretation of a single word that the prophecy receiver understands in a normal way but is meant in a slightly different fashion. Both are surprised to learn of their error while facing an armed opponent set to slay them, and both are so slain. So the similarities go beyond just the fact that both have similar prophecies: the narrative structure is much the same as well. I haven't checked a Folklore encyclopedia or anything so for the moment all I can say is analogue; but it is tempting to say source or inspiration. But I'll hold off.
A bit later in Act 4.4 Malcolm the rightful heir to the throne of Scotland and MacDuff have a chat. In this chat it is mentioned about the glorious king Edward of England. The image is practically Arthurian in nature: the perfect kingdomm that contrasts so sharply to what Scotland has become under the usurper MacBeth's rule. In this discussion Malcolm talks about "a most miraculous work in the good king". Apparently the good kind, calling on God of course, heals "strangely-visited people". He also has prophecy and "sundry blessings hang about his throne." Sound familiar Tolkienistas? Yes, it does sound rather like Aragorn, son of Arathorn: who has some gift of prophecy and foresight, who heals "strangely-visited people" with this touch apparently, and when he comes to his throne there are certainly sundry blessings.
Now some of this is typical: the whole image owes a lot to very old, traditional images of good kings. But before MacBeth and coming to know his sources (this play was written for King Jimmy I of Merry Olde...who claimed to be able to heal subjects with his touch) I had not encountered the idea of the healing by the king before. So another element to check out.
But as much as Tolkien is said not to have liked Shakespeare, (and Tolkien later clarifies this mentioning specifically the elves and faeries in Midsummer's Night Dream), it is interesting to see the number of analogues between Macbeth and LoTR.
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